Typical hot rolling mills have a high temperature steel sheet reheated up to prescribed temperatures in a slab heating furnace, and transferred on a transfer line, undergoing a series of processes such as rolling processes, before a coiling by a coiler. To implement the rolling processes, there are control amounts, such as rolling loads and rolling torques, to be adjusted in accordance with temperatures of steel sheet. It therefore is necessary to calculate temperatures of steel sheet with good precision, affording to calculate control parameters for rolling processes with good precision.
Typical hot rolling mills have wide varieties of heat transfer phenomena, such as those in steel sheet transferring processes involving heat radiation, and water cooling at a descaler, a laminar spray cooler, etc., and those in rolling processes involving machining heat generation, frictional heat generation, roll heat transmission, and heat of transformation due to phase transition in steel sheet, causing surface temperatures of steel sheet to momentarily change. Further, inside steel sheet, there is conduction of heat due to differences relative to surface temperatures, causing temperatures in steel sheet also to change. Such being the case, various boundary conditions of steel sheet are changed, so changes of surface temperatures are large, whereas inside the steel sheet, where transfer of heat attributes simply to conduction of heat, temperature changes are gradual, so there are temperature differences developed between surface temperatures and internal temperatures, rendering temperatures distributed. In particular, as the thickness of steel sheet becomes larger, such temperature distributions get larger
There are typical calculations to be made of surface temperatures of a steel sheet, where such wide varieties of changes in boundary conditions are taken into account to calculate quantities of efflux and influx heat to the steel sheet, to predict changes in surface temperatures of the steel sheet by calculation. Further, there are calculations to be made of temperatures in the steel sheet, which need a calculation of heat conduction due to temperature differences relative to the surfaces, to predict changes of internal temperatures by calculation.
Therefore, in conventional calculations of temperatures of a steel sheet, there were calculations made of quantities of efflux and influx heat through the surfaces for each boundary condition, subject to a simplification assuming an even temperature inside the steel sheet, for use of a heat capacity of the entire steel sheet to implement temperature calculations.
However, for temperatures of a state of steel sheet still thick in sheet thickness such as those in rough-rolling, there were large differences between surface temperatures and internal temperatures, so even if surface temperatures were temporarily lowered by, among others, roll heat conduction or water cooling in a descaling, such the state would be followed by risen surface temperatures due to heat conduction from inside the steel sheet, or the like, with a failure for such simplified temperature calculations as described to exactly calculate momentary changes of steel sheet temperatures.
Further, for steel sheet reheating control in a heating furnace or for thick plate rolling process or such, there were temperature calculations using a difference method, dividing a section of steel sheet into a mesh in, among others, the sheet thickness direction and the sheet width direction, taking into account heat conduction between elements, as well. However, such temperature calculation methods included dividing a section of steel sheet into a mesh, cutting also the lapse of time into time pitches, for use of a difference method to solve heat conduction equations to calculate temperatures, thus needing many calculation times, with an increased computer load, as an issue that constitute a difficulty in application of such temperature calculation methods to calculations for on-line control in actual operations of a hot rolling mill needing a real time nature.
To this point, Patent Literature 1 (JP 2001-269702 A) has proposed a method of using a difference method for temperature calculation, including depending on changes in thickness of a steel sheet such as in a rolling, to decrease a division number in a sheet thickness direction as the rolling progresses, allowing for a reduced load on the temperature calculation.